Advocates for New York City charter schools expressed outrage Monday that the state Assembly’s proposed budget aims to toughen laws requiring charters to serve sufficient numbers of hard-to-teach students.

The United Federation of Teachers said in January that pushing “anti-creaming” legislation was a priority. The budget bill released over the weekend by the Democrat-led Assembly, long allied with labor, includes harsher penalties for charters that don’t enroll and retain the same share of students who are poor, disabled...